Warning, long post
The first time I read it, back in 2012, I was bored by how long things took to get anywhere, and then how it ended before much of it even paid off, but going back into the book knowing that it's essentially filled with a ton of cliffhangers with no proper conclusions for a lot of the storylines, I can appreciate the other aspects of the book, the non-plot ones. Just like in Feast, the book focuses more on worldbuilding and character development, which is something I appreciate a lot more now than I did a decade ago. I liked Jon and Dany's struggles to rule a divided and angry people in very difficult places, having to maintain their composure despite feeling like they don't actually have any idea what the right thing to do is. It's like the opposite of Cersie's arc in Feast, where she has total confidence in herself, but constantly makes terrible decisions. Jon's final chapter is definitely one of the best chapters in the entire series, with events constantly escalating until they explode in violence and suddenly cut off. Knowing he'll almost certainly be resurrected takes away a lot of the power of this chapter, but it's still a thrilling read.
Jon's storyline was definitely my favourite of the three main characters, though I appreciated Tyrion's storyline a lot more on this re-read. His chapters with Illyrio, Griff and co. are full of very interesting dialogue that's directly relevant to the events in Westeros, and even when he's around less interesting characters (e.g. Penny, Jorah) there's still a ton of valuable worldbuilding in a part of the world that was practically ignored by Martin until this point. The descriptions of the locales in western Essos were so vivid, I can still picture the scenes so clearly, the mists and ruins of the Sorrows, the colourful lamp-lit streets of Selhorys at dusk, the old and decaying grandeur of Volantis. Martin's descriptive prose really shines in this chapters, even if they're sometimes very slow-paced and meandering. Tyrion's character-arc is also probably the best that Martin has ever written. Seeing Tyrion very gradually transform from a depressed, suicidal, hateful man that just wants to end it all into some semblance of his old self outside the walls of Meereen is very satisfying to read.
Dany's story suffers from the fact that Slaver's Bay is an abysmally awful setting, but it's not as bad as in Storm. The place feels a little less cartoonish because of more nuanced characters like Skahaz and the Green Grace. But I actually enjoyed the Meereen storyline more after Dany left, and Barristan was left to pick up the pieces. A lot of people complain that his character is bland and his storyline is unnecessary, but I really liked seeing him transform from a simple old knight to a "kingbreaker" and a Queen's Hand. The chapter where he arrests Reznak is incredibly badass and cool. I can understand why the actor that played Barristan was devastated when his character was killed off before this.
Quentyn sucks. I can't really come up with any praise for his chapters, they're boring and so is he. I think that was maybe Martin's point, but it still doesn't make for enjoyable reading.
Victarian is.... Victarian. Not much to say about him. He's a big, dumb, violent brute. Sometimes pretty entertaining in his stupidity, but he embodies pretty much every bad trait of the ironborn, which is sometimes a chore to read about. The fact that he keeps thinking he can outsmart Euron is genuinely hilarious though.
Arya is never a character I've liked, and her chapters here are no different. Braavos is an interesting city but I don't like that we have to see it through Arya's perspective. I despise her.
On the topic of Starks, I've never really cared for Bran, but his story here is a hell of a lot more interesting than in any other book. All three of his chapters have this subtly creepy and eerie feel about them, like he's unknowingly getting closer and closer to some truly dark and messed up things, but you don't quite know what it is. Very well written.
It was really nice seeing Davos again, Westeros's most down-to-earth and decent PoV character. His scene with the Lord of the Sisters, and both of his scenes with Manderly were fantastic. Davos's sense of honour and loyalty to Stannis keeps making me love him more with each passing chapter.
Melisandre's chapter was interesting but does feel a bit out-of-place since there's only one of them. I'm assuming there'll be more in Winds, which I look forward to. She's a fascinating and mysterious character, especially since Martin has said she's the most misunderstood character in the series.
Theon's storyline is unarguably one of the greatest Martin has ever written in the series, and I don't think many people would disagree with that. There really isn't anything else to add to it, everyone knows why it's so great.
Asha is meh as a character. Her PoV is only worthwhile because she's our eyes on King Stannis's northern campaign. I do kind of ship her and Ser Justin though.
Jaime's single chapter is probably my favourite chapter in the book. It's a direct continuation of my favourite storyline in the whole series - Jaime's riverlands campaign in Feast - I loved seeing him continue to act like an honourable knight, and his meeting with Lord Tytos 'Chad' Blackwood is just wonderful - like a direct contrast and polar opposite to his failed meeting with the Blackfish. Jaime's complete lack of respect for Bracken was fun too. The ending made me really sad though - seeing Jaime so happy to see Brienne, and not knowing that she's leading him into a trap. Pretty heartbreaking.
Just like the above-mentioned Jaime chapter, Cersei's two chapters should have been included in Feast, since it's the perfect ending to her story-arc, from both a structural and thematic perspective. The walk of shame chapter was a mini-masterpiece of character writing.
Areo has a chapter, although it'd be more accurate to say there's a chapter, and Areo happens to be standing in the corner while it happens. I like Doran, and am undecided on Arianne (I'm glad she finally has some respect for Doran though), but my intense hatred of the Sand Snakes brings this chapter down in my eyes. I can't believe Doran is trusting these jokes with anything.
.....oh yeah, and there's Connington. I forgot about him. That dour, stern, and utterly humourless bore. His storyline itself is one of the most interesting and potentially exciting ones in the series, it's just a shame that the guy we're seeing it through is Jon Connington. Gods, what a bore. Arianne will be drier than a Dornish desert if she has to marry him.
Overall, I really love A Dance with Dragons after this re-read. It's that extremely rare case of a fantasy book being both wide and deep as an ocean. I recognise the criticisms - too many cliffhangers, barely any conclusions, too meandering and self-indulgent - but I love it because of just how meandering and self-indulgent it is. Just like Feast, this is a deep-dive into both the world of Westeros and Essos, as well as its characters and their psychological journeys. Martin wanted to write something deeper, darker, and more thought-provoking than the original trilogy, and I think he succeeded brilliantly. This book is just so bloody massive and deep and vast, there's so much to take from it.